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PGD-based and FGSM-based are two popular adversarial training (AT) approaches for obtaining adversarially robust models. Compared with PGD-based AT, FGSM-based one is significantly faster but fails with catastrophic overfitting (CO). For mitigating CO in such Fast AT, there are two popular existing strategies: random start (RandStart) and Gradient Alignment (GradAlign). The former works only for a relatively small perturbation 8/255 with the l_\infty constraint, and GradAlign improves it by extending the perturbation size to 16/255 (with the l_\infty constraint) but at the cost of being 3 to 4 times slower. How to avoid CO in Fast AT for a large perturbation size but without increasing the computation overhead remains as an unsolved issue, for which our work provides a frustratingly simple (yet effective) solution. Specifically, our solution lies in just noise augmentation (NoiseAug) which is a non-trivial byproduct of simplifying GradAlign. By simplifying GradAlign we have two findings: (i) aligning logit instead of gradient in GradAlign requires half the training time but achieves higher performance than GradAlign; (ii) the alignment operation can also be removed by only keeping noise augmentation (NoiseAug). Simplified from GradAlign, our NoiseAug has a surprising resemblance with RandStart except that we inject noise on the image instead of perturbation. To understand why injecting noise to input prevents CO, we verify that this is caused not by data augmentation effect (inject noise on image) but by improved local linearity. We provide an intuitive explanation for why NoiseAug improves local linearity without explicit regularization. Extensive results demonstrate that our NoiseAug achieves SOTA results in FGSM AT. The code will be released after accepted.